| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Binomial with complementary events |
| Difficulty | Standard +0.3 This is a straightforward S1 binomial distribution question with standard hypothesis testing. Part (i) is trivial expectation recall (E=np), parts (ii)(a-b) are routine binomial probability calculations using tables or formula, and part (iii) is a textbook one-tailed hypothesis test with clear setup. All techniques are standard S1 content with no novel problem-solving required, making it slightly easier than average overall. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
Mark is playing solitaire on his computer. The probability that he wins a game is 0.2, independently of all other games that he plays.
\begin{enumerate}[label=(\roman*)]
\item Find the expected number of wins in 12 games. [2]
\item Find the probability that
\begin{enumerate}[label=(\alph*)]
\item he wins exactly 2 out of the next 12 games that he plays, [3]
\item he wins at least 2 out of the next 12 games that he plays. [3]
\end{enumerate}
\item Mark's friend Ali also plays solitaire. Ali claims that he is better at winning games than Mark. In a random sample of 20 games played by Ali, he wins 7 of them. Write down suitable hypotheses for a test at the 5\% level to investigate whether Ali is correct. Give a reason for your choice of alternative hypothesis. Carry out the test. [9]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q8 [17]}}